Local convexity in CAT(\kappa)-spaces
Metric Geometry
2014-09-24 v2
Abstract
Heinrich Tietze has shown that for a closed connected subset of euclidean space being convex is a local property. We generalize this to CAT(0)-spaces and locally compact CAT(\kappa) spaces. As an application we give a construction of certain convex sets in euclidean buildings.
Cite
@article{arxiv.1211.1871,
title = {Local convexity in CAT(\kappa)-spaces},
author = {Kai-Uwe Bux and Stefan Witzel},
journal= {arXiv preprint arXiv:1211.1871},
year = {2014}
}
Comments
13 pages, 2 figures; v2 added references